Phase-3 Local Term Closure and the Copper Bridge: Supplementary Numerical Certificates

This archive contains the supplementary numerical certificate files for the manuscript “Phase-3 Local Term Closure and the Copper Bridge: From Atomic Shell Geometry to Nonlocal Response.” The supplementary notebook collects and verifies the numerical closure chain used in the paper. It records the strict local Phase-3 closure of chromium, the best strict one-center copper residual, and the resulting Phase-4 copper bridge threshold. The certificate verifies: Pi_Cr_strict = -4.012884 eV, Pi_Cu_1c = +0.198205 eV, and the copper bridge condition Omega_nl_Cu > 0.198205 eV. The included CSV files summarize the main closure certificate, guardrail logic, phase status, bridge thresholds, and reader checklist. The notebook does not fit closure energies to external spectroscopic data. External atomic data are used only for standard configurations, term labels, and unit conversion in the accompanying manuscript. This archive is intended as a compact reproducibility supplement. The larger computational notebooks used to generate the intermediate radial, selected-CI, screening, and guardrail calculations are treated as the computational archive.